A particularly advantageous vacuum cleaner system has at least two filters and self-cleans its filters via back-flushing, without needing to stop normal operation to self-clean. Also, a self-cleaning valve assembly is provided for use in a vacuum cleaner. Also, a vacuum cleaner is provided that uses permanent, self-cleaning filters, and does not need disposable filters or filter bags, and advantageously can use inexpensive plastic bags. In another vacuum cleaner system, waste is collected in an ordinary plastic bag without any special preparation or modification of the bag being needed. Further, an inventive self-cleaning X-valve assembly cleans itself and is useable in the vacuum cleaner system.